A posteriori stopping in iteratively regularized Gauss–Newton type methods for approximating quasi-solutions of irregular operator equations

We consider a class of iteratively regularized Gauss–Newton type methods for approximating quasi-solutions of irregular nonlinear operator equations in Hilbert spaces. We assume that the Frechet derivative of the problem operator at the desired quasi-solution has a closed range. We propose an a-posteriori stopping rule for the considered methods and get an accuracy estimate which is proportional to the error level of input data.